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Filtering and Model Reduction of PDAEs with Stochastic Boundary Data
Author(s) -
Stahl Nadine,
Marheineke Nicole
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900130
Subject(s) - reduction (mathematics) , hierarchy , boundary (topology) , pipeline (software) , state (computer science) , model order reduction , mathematics , computer science , data reduction , algebraic number , partial differential equation , mathematical optimization , algorithm , data mining , geometry , mathematical analysis , projection (relational algebra) , economics , market economy , programming language
In this paper we investigate state reconstruction for gas pipeline networks using model hierarchies derived from model order reduction techniques. The pipeline network is described by partial differential algebraic equations (PDAEs), for which model order reduction was extensively studied in [1]. We use and extend upon the aforementioned results to estimate the system state, when the boundary data is perturbated by an Ornstein‐Uhlenbeck process. We study the performance of state reconstruction based on the derived model hierarchy. Of special interest, hereby, is the relationship between the quality of the state estimation and the underlying reduced order model.